1.  Spotting and Valuing Options Principles of Corporate Finance Brealey and Myers Sixth Edition Slides by Matthew Will Chapter 20 © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill

2. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 2 Topics Covered  Calls, Puts and Shares  Financial Alchemy with Options  What Determines Option Value  Option Valuation

3. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 3 Option Terminology Call Option Right to buy an asset at a specified exercise price on or before the exercise date.

4. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 4 Option Terminology Put Option Right to sell an asset at a specified exercise price on or before the exercise date. Call Option Right to buy an asset at a specified exercise price on or before the exercise date.

5. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 5 Option Obligations

6. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 6 Option Value  The value of an option at expiration is a function of the stock price and the exercise price.

7. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 7 Option Value  The value of an option at expiration is a function of the stock price and the exercise price. Example - Option values given a exercise price of $85

8. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 8 Option Value Call option value (graphic) given a $85 exercise price. Share Price Call option value 85 105 $20

9. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 9 Option Value Put option value (graphic) given a $85 exercise price. Share Price Put option value 80 85 $5

10. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 10 Option Value Call option payoff (to seller) given a $85 exercise price. Share Price Call option $ payoff 85

11. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 11 Option Value Put option payoff (to seller) given a $85 exercise price. Share Price Put option $ payoff 85

12. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 12 Option Value Protective Put - Long stock and long put Share Price Position Value Long Stock

13. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 13 Option Value Protective Put - Long stock and long put Share Price Position Value Long Put

14. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 14 Option Value Protective Put - Long stock and long put Share Price Position Value Protective Put Long Put Long Stock

15. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 15 Option Value Protective Put - Long stock and long put Share Price Position Value Protective Put

16. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 16 Option Value Straddle - Long call and long put - Strategy for profiting from high volatility Share Price Position Value Long call

17. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 17 Option Value Straddle - Long call and long put - Strategy for profiting from high volatility Share Price Position Value Long put

18. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 18 Option Value Straddle - Long call and long put - Strategy for profiting from high volatility Share Price Position Value Straddle

19. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 19 Option Value Straddle - Long call and long put - Strategy for profiting from high volatility Share Price Position Value Straddle

20. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 20 Option Value Upper Limit Stock Price

21. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 21 Option Value Upper Limit Stock Price Lower Limit (Stock price - exercise price) or 0 whichever is higher

22. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 22 Option Value Components of the Option Price 1 - Underlying stock price 2 - Striking or Exercise price 3 - Volatility of the stock returns (standard deviation of annual returns) 4 - Time to option expiration 5 - Time value of money (discount rate)

23. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 23 Option Value Black-Scholes Option Pricing Model O C = P s [N(d 1 )] - S[N(d 2 )]e -rt

24. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 24 O C = P s [N(d 1 )] - S[N(d 2 )]e -rt O C - Call Option Price P s - Stock Price N(d 1 ) - Cumulative normal density function of (d 1 ) S - Strike or Exercise price N(d 2 ) - Cumulative normal density function of (d 2 ) r - discount rate (90 day comm paper rate or risk free rate) t - time to maturity of option (as % of year) v - volatility - annualized standard deviation of daily returns Black-Scholes Option Pricing Model

25. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 25 (d 1 )= ln + ( r + ) t PsSPsS v22v22 v t 32 34 36 38 40 N(d 1 )= Black-Scholes Option Pricing Model

26. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 26 (d 1 )= ln + ( r + ) t PsSPsS v22v22 v t Cumulative Normal Density Function (d 2 ) = d 1 -v t

27. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 27 Call Option Example What is the price of a call option given the following? P = 36r = 10%v =.40 S = 40t = 90 days / 365

28. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 28 Call Option (d 1 ) = ln + ( r + ) t PsSPsS v22v22 v t (d 1 ) = -.3070N(d 1 ) = 1 -.6206 =.3794 Example What is the price of a call option given the following? P = 36r = 10%v =.40 S = 40t = 90 days / 365

29. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 29 Call Option (d 2 ) = -.5056 N(d 2 ) = 1 -.6935 =.3065 (d 2 ) = d 1 -v t Example What is the price of a call option given the following? P = 36r = 10%v =.40 S = 40t = 90 days / 365

30. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 30 Call Option O C = P s [N(d 1 )] - S[N(d 2 )]e -rt O C = 36[.3794] - 40[.3065]e - (.10)(.2466) O C = $ 1.70 Example What is the price of a call option given the following? P = 36r = 10%v =.40 S = 40t = 90 days / 365

31. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 31 Put - Call Parity Put Price = Oc + S - P - Carrying Cost + Div. Carrying cost = r x S x t

32. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 32 Example ABC is selling at $41 a share. A six month May 40 Call is selling for $4.00. If a May $.50 dividend is expected and r=10%, what is the put price? Put - Call Parity

33. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 20- 33 Example ABC is selling at $41 a share. A six month May 40 Call is selling for $4.00. If a May $.50 dividend is expected and r=10%, what is the put price? Put - Call Parity Op = Oc + S - P - Carrying Cost + Div. Op = 4 + 40 - 41 - (.10x 40 x.50) +.50 Op = 3 - 2 +.5 Op = $1.50